I want to filter the following objects by category_id using the following array of category_id values:
[19012000, 19012001, 19012002, 19012003, 19012004, 190
I don't see any reason to use _.first here? The rest of your filter statement looks good, altough you may swap the indexOf call for _.contains:
indexOf
var postDates = _.filter(goodDates, function(n){ return _.contains(category_id, n.category_id); });